Study On Several Key Problems Under Characteristic Relation Based Rough Sets

The classical rough set is only to deal with data in information systems that is precise and complete. However, in the real applications, many data sources have dynamic characteristics, and the data in the information systems can be incomplete. The classical rough set theory is no longer valid for dealing with this kind of practical problems. Characteristic relation based rough set model which can deal with lost and "do not care" values was proposed. It supports knowledge discovery from incomplete information systems. In this paper, several key problems under characteristic relation based rough set model are investigated.Firstly, knowledge reduction algorithms based on discernibility matrix, information entropy and granularity, etc, are presented under the characteristic relation. Examples are employed to illustrate that the validation of the algorithms. At the same time, the relation of the information entropy and knowledge granularity is discussed, and the equivalence of knowledge reduction with respect to information entropy and granularity is proved.Secondly, the approximations of concepts may vary when the information system is dynamically changing. This paper only considers the situation that attribute value dynamically change in the information system. According to the idea of the granularity, the definitions of attribute values coarsening and refining in incomplete information systems are given. Then approaches for updating the approximations are discussed when attribute values coarsening and refining under the characteristic relation. Finally, examples are given to illustrate the validity of the proposed approaches.Finally, through analyzing and comparing the characteristic relation, tolerance relation and non-symmetrical similarity relation, we find that there are some shortcomings in the characteristic relation. In order to solve these problems effectively, three new characteristic relations:A, B and C characteristic relations are presented. This paper further discusses the variation of the approximations under A, B and C characteristic relations. At the same time, several theorems are given and several examples are employed to illustrate the theorems.